During this time, it was not unusual for me to get very little sleep many days in a row. As a coping mechanism, I learned somewhat to "half-sleep", where I would close one eye and relax that side while continuing to do things using the other eye.
I wouldn't consider it sleeping just on one side of the brain, but there was definitely something different going on. I found that 2-4 hours of that would help my overall wakefulness.
Fortunately I had my condition addressed, but it would have been interesting to see if over time I would have developed into a full sleep-wake state of consciousness.